13646 ÷ 5 = 2729 R1
Alright, let's work through the division of 13646 by 5 step by step.

Step 1:
5 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 5

Step 2:
5 goes into 13 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 10 from 13 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 5

Step 3:
5 goes into 36 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 27
Subtract 35 from 36 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 5

Step 4:
5 goes into 14 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 272
Subtract 10 from 14 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 5

Step 5:
5 goes into 46 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 2729
Subtract 45 from 46 to get 1.

The final result is 2729 with a remainder of 1.